I'm new in this forum and I came here because I want to move to Helsinki and I have many doubts...

I think that first I have to talk about my history and then I'm sure that I will get more tips about how to do it.

I'm Electronic Engineer and I came to Helsinki two years ago to work with my actual company, from Spain, in the new metro of the city (my company is the manufacturer of this metros). During this time I met my actual couple, but one year ago when the project ended, I had to come back and nowadays we are having a distance relationship. During all this time, I was looking for work, currently still looking, but I can't find anything... which is hopeless...

We have taken the decision if I can't find anything in one month, me to leave my actual company and go there to live and keep looking directly there (I have some savings and with it and the payment of my unemployment salary I think we can survive).

We are not still married, and we want to wait because she is not working currently and the government is giving to her an aid to pay the flat. She has two kids and she is not getting almost anything from the father of the kids. We thought about the possibility she to come to Spain with kids, but it's almost impossible, her ex doesn't allow her to take kids to Spain... then the solution is me to move there. I'm very happy with the idea of moving to Helsinki because I love this city, the only problem is to find a working place.

My question is how I can do to get my Residence permit if we are not married yet and we don't have any other family ties.

Also, I have a car that I would like to take it with me. I bought it 7 months ago and I would like that if it's necessary to pay taxes, I have read that having bought your car 6 months before going, is exempt to pay taxes, that's right? If I have to pay, I think is a better idea to sell it and buy another one there, but I would like to know how much time I can drive my car in Finland before selling it (of course I will sell it in Spain), because I need a car for some time.

If you have any other tips, please, write me, I'm completely desperate to move there and have a great life with my small new family.

Since you are moving from an EU country, things will be easier. You can freely move in Europe but this doesn't give you any right to permanent residence.
The immigration officers will not see any good reason for you to move, so I suggest you take proof of your savings, to prove you can support yourself, otherwise they'll never register you as resident.